Simplify the following expression: $ x = \dfrac{z - 3}{z - 4} + \dfrac{-8}{9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{z - 3}{z - 4} \times \dfrac{9}{9} = \dfrac{9z - 27}{9z - 36} $ Multiply the second expression by $\dfrac{z - 4}{z - 4}$ $ \dfrac{-8}{9} \times \dfrac{z - 4}{z - 4} = \dfrac{-8z + 32}{9z - 36} $ Therefore $ x = \dfrac{9z - 27}{9z - 36} + \dfrac{-8z + 32}{9z - 36} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{9z - 27 - 8z + 32}{9z - 36} $ $x = \dfrac{z + 5}{9z - 36}$